Weird vertices on subsurf modifier
The problem is due to faces with more than 4 vertices as the subsurf can only work with triangles (3 vertices) and quads (4 vertices).

Faces with more than 4 vertices are known as 'ngons' (basically 'polygon' with with the 'poly' replaced with 'n' to represent any number (greater than 4) - I can see two towards the top-centre of your image and it is those that are causing the issue.

The solution is to adjust the geometry to replace those faces with tri and quad faces. The easiest way to achieve this would be to simply cut one of the corners off to a tri, leaving a quad.